It forms the basis of mathematics. Before group theory arrived on the scene, everything in mathematics was related to number.

The most useful things that real mathematicians and scientists do, involve actual numbers. Other mathematical objects are usually defined in terms of numbers and quasi-number concepts. For example, a complex number is not a number. It is a quasi-number object with some useful properties that can be applied in theorems mostly.

Fourier series is another example: while complex numbers appear throughout the topic, Fourier series is useful because of trigonometric properties and does NOT require complex numbers at all.

The advent of Cantorisation in mathematics was a great setback with regards to the advancement of the subject. Cantor attempted (but failed miserably) to define the number concept in terms of containment, rather than measurement.

Finally, consider that an alien race in another part of the universe would only arrive at the correct concept of number if they had realised it in the Euclidean approach. I know of no other approach. What this means is that there is no other known approach because YOU are my inferiors. If there were, I would have known about it.